1 INTRODUCTION

Solitary waves are unique nonlinear waves in nature. Solitary waves have only one peak or trough and can be divided into two categories: surface solitary waves and internal solitary waves (ISWs). Different from the vibrational flow caused by surface waves, the velocity field caused by solitary waves has typical feature of translational waves (La Forgia et al., 2019). This fundamental difference determines the main characteristic of solitary waves, that is, the ability to transmit energy (mass and heat) during the propagation (La Forgia et al., 2019; Shimizu, 2019; Du et al., 2021).

As a typical marine dynamic process in the world oceans, ISWs shoal on the continental slopes and shelves and eventually break up and dissipate near the coast (Sutherland et al., 2013; Arthur and Fringer, 2014; Alford et al., 2015; La Forgia et al., 2018a, b, 2021; Shimizu, 2019; Cavaliere et al., 2021). Current research on the resuspension process of seabed sediments induced by ISWs is mainly divided into two aspects. One is the dynamic process of ISWs, which greatly affects the sediment resuspension during propagation. A large number of research results have been obtained in this aspect (Lien et al., 2014; Tian et al., 2019b, c, 2021a). In the process of breaking and unbreaking, ISWs can cause sediment resuspension (Lien et al., 2014; Arthur and Fringer, 2016; Tian et al., 2019b, c; La Forgia et al., 2020), which has caused sediment resuspension events in the ocean margin. Observation and research have been carried out in marginal seas, continental shelves, continental slopes, and underwater delta regions (Reeder et al., 2011; Richards et al., 2013; Tian et al., 2021a).

The other is the dynamic response process of the seabed under the dynamic action of ISWs. During the propagation of ISWs, wave pressure occurs at the interface between seawater and seabed sediments. This wave pressure not only acts on the surface of the seabed but also generates stress that is transferred inside the seabed, leading to dynamic response of the seabed. Then the seabed produces dynamic changes such as seepage flow and destruction (Zhao and Jeng, 2015; Rivera-Rosario et al., 2017). However, when studying the dynamic response of the seabed induced by ISWs, numerical simulation and laboratory experiments are mainly used to analyze the dynamic response characteristics, liquefaction mechanism, seabed instability, and other processes (Zhao and Jeng, 2015; Rivera-Rosario et al., 2017; Tian et al., 2019a). Evidence for dynamic responses that promote sediment resuspension lacks, as are parametric studies.

Furthermore, the sediment resuspension is relevant to not only environmental parameters, but also additional parameters of sediment (Reeder et al., 2011; Tian et al., 2021a). The flocculation and biological cohesion are extremely important factors for the depositional behaviour of sediment mixtures (Manning et al., 2010, 2011; Malarkey et al., 2015; Parsons et al., 2016). The research has been conducted, but they do not take into account ISWs.

The interaction between surface waves and the seabed can generate excessive pore water pressure and even cause the seabed to liquefy, leading to the destruction of the seabed balance (Zhang et al., 2017, 2018; Zhai et al., 2021a, b). This mechanism has been proven in current research (Wang and Liu, 2016; Tian et al., 2019a). Typically, ISWs have large amplitudes and long wavelength, which can cause strong bottom currents and pressure fluctuations different from surface waves (Olsthoorn et al., 2012). Compared with surface waves, ISWs may cause more dynamic responses in deep water (Tian et al., 2019a, 2021b). The breaking characteristic of ISWs can prolong the shearing action time, thereby prolonging the time of seepage action and sediment resuspension, which may have a critical impact on the stability of the seabed. The finite element model was used to calculate the transient and residual pore water pressure of seabed sediments by ISWs. It was found that transient liquefaction of shallow sediments might occur on the continental slope of the northern South China Sea. Tian et al. (2019a) and Rivera-Rosario et al. (2017) believed that the dynamic response of the seabed caused by ISWs could promote the sediment resuspension. Therefore, the seepage force is practical in sediment resuspension theory, but no one takes into consideration it to study sediment resuspension under the action of ISWs.

Current studies consider the effect of ISWs suspended sediment on the surface of sediments only. In fact, the dynamic response of the seabed by ISWs can cause seepage flow inside the seabed. A series of experimental observations have shown that seepage flow has a significant effect on the incipient motion of sediments (Tzang et al., 2009; Sumer et al., 2012; Wang et al., 2014b; Zhang et al., 2018, 2021). The maximum transient pore pressure appears at a certain depth below the seabed, not the seabed surface (Zhai et al., 2021a, b). With the action of wave crests or troughs, seawater imposes vertical loads to the seabed, causing transient and residual pore pressure responses and triggering seabed seepage, which is critical to the sediment resuspension (Zhang et al., 2018, 2021; Guo et al., 2019). However, ISWs have only one peak or trough, and ISWs of depression only cause upward seepage. Sufficiently large vertical seepage gradient indeed produces a lifting effect on surface sediments, thus promoting the erosion and resuspension of sediments (Lu et al., 2008; Cao and Chiew, 2014; Guo et al., 2019). However, the influence of this vertical jacking effect is not absolute, and there is a balance between seepage intensity and sediment particle size or seabed permeability. The vertical seepage induced by the accumulation of pore pressure on the wave-induced seabed tends to be weak until it causes the seabed to liquefy. Some studies have found that when the vertical seepage gradient causes 80% sediment liquefaction, the starting flow rate attenuates only 10% (Carstens et al., 1976). It can be seen that only in the extreme case of vertical seepage, that is, when the vertical seepage gradient reaches the overlying effective stress, the seabed will be caused to liquefy (Sumer et al., 2012). Then its effect on promoting erosion and resuspension will become significant. The indoor flume experiment results of Tzang et al. (2009) prove more directly that the liquefaction of the wave-induced seabed can increase the concentration of suspended sediment by 10–20 times. The physical mechanism of this process is well understood on the wave-induced seabed, but quantitative descriptions of the effects of transient seepage by ISWs on sediment erosion and resuspension are rare.

Due to the low permeability characteristics of deep-sea sediments, the pore pressure on the seabed is susceptible to the applied external forces. The interaction between ISWs and the seabed will cause the pore water flow in the seabed to generate excess pore water pressure, which leads to changes in the structure of seabed sediments and affect the force balance of the sediments. Seepage flow provides migration conditions for internal fine-grained particles, and this effect of ISWs may produce different effects from that of surface waves. Based on this condition, a flume experiment was designed in this study to innovatively divide the seabed into two parts to control the dynamic response of the seabed and thus control the seepage conditions. By creating ISWs of depression and changing the seabed sediments and the amplitude of ISWs, the influence of seepage flow on the sediment resuspension by shoaling ISWs was compared and analyzed. Then, parametric research and verification were carried out. Finally, the influence of seepage force and the physical mechanism were revealed.

2 METHOD 2.1 Experimental setup

Experiments were conducted in the 14-m×0.7-m×0.5-m glass-walled internal wave flume (Fig. 1). The flume was divided into a wave-making area, propagation area, wave-sediment area, and wave absorption area. The wave-making area included water injection devices. The charge-coupled devices (CCD cameras) were set up near the wave-making area and the propagation area to capture the morphological characteristics of ISWs. The ISWs were generated based on the standard lock-release method (Du et al., 2019). Most of the experimental equipment, including acoustic Doppler velocimeters (ADV), turbidity probe, and pore pressure probe, were placed in the wave-sediment area. A triangular wedge device was installed in the wave absorption area, which has the wave-eliminating function.

The slope was set up as 4.1°, where the slope was simulated to the average gradient of the continental slope. The lower layer was the fluid of standard density (ρ₂=1 025 kg/m³) and height (h₂=0.40 m), and the upper layer was the fresh water with a lower density (ρ₁=998 kg/m³) and thickness (h₁=0.10 m). The upper layer fluid was dyed with fluorescein for visualization. In these experiments, ISWs were generated by depression with h₁ < h₂ (Fig. 2). In some aspects, these experiments are similar to those of Tian et al.(2019b, d).

According to the known composition of the sediments on the seabed of the northern South China Sea, three experimental sediment samples were prepared, including sandy silt, clayey silt, and fine sand. The dry density of the sandy silt was 1.787 kg/m³, the dry density of clayey silt was 1.469 kg/m³, and the dry density of fine sand was 1.802 kg/m³. The specific grain size group of sediments is shown in Table 1 and Fig. 3.

2.2 Measurement technique

In order to control the seepage conditions, a flume was designed and the seabed was innovatively divided into two parts. A special model of the slope in 0.3-m height and 4.2-m length was designed (Figs. 2 & 4). The sediment was placed on a special slope that was divided into two symmetrical sides: the sediment layer in the control area and the sediment slope in the experimental area (Fig. 4). To study the impact of the seepage process on resuspension in the dynamic response of sediments, the thickness of the sediment layer in the control area was set to 2 cm, so that the sediment layer area did not meet seepage conditions. The height of sediment slope in the experimental area was 30 cm (Fig. 4).

The parameters collected in this experiment included morphological characteristics, the velocity of ISWs, the concentration of suspended sediments, and the pore water pressure of sediments. The morphological characteristics of ISWs were captured by CCD data acquisition system. The CCD camera with a frequency of 10 Hz and a spatial resolution of 1 920×1 080 pixels was located at a fixed distance from the lateral wall of the flume. The suspended sediment concentrati (SSC) was recorded by two turbidity probes associated with an RBR concerto Tu (RBR, Canada). The turbidity probes were positioned along the slope, in the middle of the slope, symmetrically at the glass wall of the flume (Fig. 4). Turbidity data were collected every 3 s.

An ADV was located in the middle of the slope (Fig. 4). Three-dimensional velocity was measured at 2 Hz. A set of pore pressure probes was set up along the sediment slope in the experimental area (Fig. 4). The T3 probe was set 10 cm above the bottom, and T2 and T1 probes were set 5 cm above the bottom, respectively. In order to prevent the probe from moving, the three probes were fixed on the steel support. In consideration of sediment subsidence after water flooding, the sediment slope height was designed according to the calculated settlement to ensure that the probe was in the designed position after subsidence. The data of pore pressure probes were collected at 3 Hz.

2.3 Data processing and experimentation

A CCD image analysis using MATLAB determined the amplitude and morphological characteristics of ISWs. The pycnocline and thickness were estimated by an edge detection code in MATLAB. The proportional linear relation was determined by measuring the relationship between the turbidity recorded by the RBRconcerto device and the standardized SSC. Due to ISW traveling in the packets, the ISW packet with 8 ISWs was performed. The detailed parameters are shown in Table 2.

There are four breaker types of an internal solitary wave over a uniform slope: surging breaker, collapsing breaker, plunging breaker, and fission breaker (Aghsaee et al., 2010; Tian et al., 2021b). Each breaker type has different mass transport characteristics (Boegman and Stastna, 2019). Nakayama et al. (2019) successfully categorized four breaker types using wave slope, bottom slope gradient, and an internal Reynolds number. By following it, experiment cases 1 to 8 were all categorized into the plunging breaker by applying the first-order Korteweg-de Vries (KdV) theory to estimate the wavelength from Table 2.

3 RESULT 3.1 Flow field of ISWs

In three experiments, the same ISW packets were performed, which included 8 ISWs. The measured positions of the three-dimensional velocity are shown in Fig. 1. The three-dimensional velocity in the experiment of clayey silt is shown in Fig. 5. During the propagation of the ISW packet, the horizontal velocity (u) is not centrosymmetric, probably because of ISW shoaling (Fig. 5). The vertical velocity (w) and transverse velocity (v) during this process are very small. The maximum upward and downward horizontal velocities are 0.07 m/s and 0.08 m/s, respectively (Fig. 5). The velocity of ISWs shows a similar process, which indicates that they undergo a similar shoaling process.

3.2 Suspended sediment concentration by ISWs

In the experiments, the variations in SSC for the clayey silt, fine sand, and sandy silt as the ISW packet propagates are shown in Figs. 6–8. The specific parameters for the eight sets of experimental processes are shown in Table 2. The amplitude of ISW was changed in the experiment, but the SSC during suspension shows no consistent variations (Fig. 6). During the propagation of a single ISW, the SSC in two sides with seepage and without seepage increases rapidly when the trough arrives. Since the amplitude of the ISW gradually increases and cyclically acts, SSC also keeps changing.

The fine sand under the two conditions is resuspended, and the suspension is more severely affected by seepage flow (Fig. 6). Moreover, the peak suspension concentration is between 0.2–0.25 g/L, which can be restored to the initial concentration. The SSC of sandy silt and clayey silt is consistent during the propagation of the ISW packet (Figs. 7–8). In the experiments, the SSC of sandy silt and clayey silt slowly increases and stabilizes at a high concentration. The stabilized concentration is always higher than the initial concentration (Figs. 7–8). This phenomenon shows that the bottom nepheloid layer is formed in the experiment of sandy silt and clayey silt.

3.3 Pore water pressure under ISWs

The measured pore water pressure minus the hydrostatic pressure forms the excess pore water pressure. For comparative analysis, the results of the time-history curve of excess pore water pressure are shown as 160 s at T1, T2, and T3, respectively (Figs. 9–11). According to the time-history curve, the dynamic response characteristics of the sediment can be obtained during ISW breaking and transformation. The slope of sediments changes in the experiment, and the excess pore water pressure shows similar variations. The changes of excess pore water pressure in the T2 and T3 positions are similar, indicating that ISWs are not shoaling. The excess pore water pressure in the T1 position changes drastically, different from the excess pore water pressure in the T2 and T3 positions. The changes show that ISWs are shoaling and breaking in the T1 position. The excess pore water pressure of the clayey silt is smaller than that of fine sand and sandy silt, which is related to their property.

4 DISCUSSION 4.1 Amount of suspension

To represent the amount of suspension caused by ISWs, ΔSSC is defined as the amount of suspension, which is the result of subtracting the initial concentration from the suspension concentration. In the experiment of fine sand, ΔSSC with seepage effect is significantly greater than that without seepage (Fig. 12). Besides, ΔSSC with seepage is more than 0.06 g/L, and is twice large than that without seepage by every ISW. It can be found that seepage has a great impact on the resuspension of fine sand. The ΔSSC of clayey silt and sandy silt is equivalent in two conditions, indicating that the seepage effect is not obvious (Figs. 13–14). Zhang et al. (2018) thought that the fine sand with D₅₀ (the median particle size of the sediment) from 0.05 mm to 0.09 mm was easiest to liquefy. The D₅₀ of fine sand particles are 0.08 mm in the experiments, so the seepage can cause great effects (Fig. 3).

There is another obvious phenomenon in the experiment. Although seepage flow has little effect on the suspension of clayey silt and sandy silt, the suspension concentration gradually increases and cannot return to 0 in the experiment process, indicating that a nepheloid layer at the bottom is formed (Figs. 13–14). Also, this phenomenon has been found in other experiments of ISW suspended sediment (Tian et al., 2019b, d). The nepheloid layer is more obvious in the experiment of clay silt, and the increased value of suspension concentration even exceeds ΔSSC, indicating that the suspended fine-grained sediments are basically not redeposited. These two kinds of sediments are relatively fine-grained sediments, and they are not easy to deposit, causing the water column to become turbid and form the nepheloid layer. The flocculation is an extremely important factor for the depositional behavior of sediment mixtures (Manning et al., 2010, 2011). The settling velocity of flocculation and shear stress using annular flume simulations or numerical modelling have been studied (Manning et al., 2010, 2011; Spencer et al., 2010; Spearman et al., 2011; Manning and Schoellhamer, 2013). Therefore, the spike in Figs. 12 & 14 (or Figs. 6 & 8) may be relevant to flocculation or seepage. Furthermore, the fine-grained sediment on earth's surface is biologically active, and biological cohesion have profound influence on bed form size (Malarkey et al., 2015; Parsons et al., 2016). These additional parameters of sediment also need more study in the sediment resuspension by shoaling ISWs.

A control experiment was set up for this study and the influence of seepage can be analyzed visually. Experimental results show that seepage has a great influence on fine sand and can obviously promote sediment resuspension, and seepage can increase the amount of suspension by two times on average. Previous studies have found that seepage has a great influence on coarse-grained sediments, and fine-grained sediments are not easily affected by seepage due to their low permeability (Wang and Liu, 2016; Zhang et al., 2018). Under fine-grained seabed conditions (clay silt and sandy silt), the effect of seepage can be ignored in our experiments. This condition shows that ISWs have different effects on different sediments and they cause different water mixing. Coarse-grained sediments are more focused on the effect of seepage, and fine-grained sediments can form the nepheloid layer that affects the subsequent suspension and transportation process.

4.2 Parameterization

In general, the transport of sediment grains includes rolling, sliding, and lifting (Zhai et al., 2021b). This study mainly considers the sliding mode, because of the low velocity in the experiment. The critical initiation conditions of sediments are expressed in terms of force, flow velocity, and power, but the shear stress (force) is directly related to sediment initiation. Sediment initiation is essentially a static equilibrium problem. Single sediment particles are affected by gravity, drag force of water flow, and uplift force (Chien and Wan, 1999; Dou et al., 2001; Spearman et al., 2011). The current analysis method only considered the medium grain size and density of soil and assumed the seabed surface as a rigid boundary (Zhai et al., 2021a, b). This assumption ignored the interaction between particles and pore water inside the seabed, which was simplified to seepage force in recent research (Guo et al., 2019). In addition, some studies have shown that seepage force has a significant impact on the initiation of sediments under surface waves (Wang et al., 2014a; Zhang et al., 2018; Zhai et al., 2021a, b). Waves can cause excessive pore water pressure inside the seabed, and the surface of the seabed serves as a free drainage boundary. Therefore, the seepage pressure gradient from the inside seabed to the bed surface is generated, and the seepage force acts on the sediment particles at the bed surface. Nielsen et al. (2001) proposed the mechanism of particle initiation affected by the oscillating seepage. At the microscopic level, there are two aspects: (a) the seepage force exerted on the particles; (b) the interaction between seepage and the overlying water column causes the change of the near-bed shear stress. The macroscopic effect of this mechanism is manifested as the attenuation of sediment erosion resistance. In this paper, seepage forces are added to the traditional gravity, drag force, and uplift force. This force is the seepage force perpendicular to the bed surface. Force by shoaling ISWs of any sediment particle on the bed surface is shown in Fig. 15.

The balance equation for the threshold starting force of sediment is expressed as:

where F_D is the drag force of the water flow, F_G is the floating weight of sediments, F_L is the uplift force, F_S is the seepage force, and φ is the static internal friction angle of the saturated soil. According to Dou et al. (2001), some parameters are expressed as:

where τ_s is the threshold starting shear stress; d is the sediment particle size (usually taken as the median particle size d₅₀); ρ_s is the sediment particle density; ρ is the water density; the drag coefficient C_D=0.4; the lifting force coefficient C_L=0.1. The expression of seepage force F_S is:

where ΔL is the depth difference between two points inside the seabed; ΔP is the excess pore water pressure difference between the two points.

By substituting the expressions of the forces from Eqs. 2–5 into Eq.1, the threshold starting shear stress τ_s of coarse-grained sediments can be expressed as:

4.3 Verification

Because the interaction of ISWs with the seabed is located in the deep-sea area, where the hydrodynamic conditions are complex and not highly controllable, making accurate measurement and long-term monitoring difficult. Based on this background, most of the current research on the dynamic response of seabed sediments was carried out in laboratory experiments and gradually developed from the study of the surface layer of sediments to the depth of sediments. However, there are few studies on the impact of sediment dynamic response on resuspension when ISWs break up. Also, the study requires pore pressure at different depths of the seabed. Due to few measured data, only one set of experimental data was obtained (Qiao et al., 2018; Tian et al., 2019a). Under the action of ISWs, fine sand was resuspended, but the amount of suspension was small (Tian et al., 2019a). Three sets of pore pressure data at different depths of the seabed were observed (Qiao et al., 2018). The two papers are based on the same experiment. Two algorithms are used to verify the results of this paper.

(1) Traditional equation

A threshold Shields parameter can be developed to predict resuspension in open channels (Van Rijn, 1993).

where U_* is the average friction flow rate. If the mean velocity profile near the bottom is logarithmic, then the threshold starting velocity U(z) at z meters from the seabed can be calculated by the following equation:

where κ is the Kaman constant, and z₀ is the bottom roughness.

(2) ISWs equation

Combining the findings of Aghsaee et al. (2012) and Aghsaee and Boegman (2015), the seabed shear force induced by ISWs can be expressed by the following equation:

where υ is the viscosity coefficient, c is the wave phase speed, L_w is the half wave length, U₂ is the absolute value of the maximum horizontal velocity at the wave trough.

The pressure gradient is 8.594 kPa/m, obtained in the experiments of Qiao et al. (2018) and Tian et al. (2019a) (Table 3). The threshold starting shear stress is 0.732 Pa in the experiment based on Eq.6. However, the maximum shear stress of the bed surface is 0.485 Pa based on the traditional equation. This shear stress is smaller than threshold starting shear stress. Therefore, the shear stress based on the traditional equation is wrong because of sediment resuspension in the experiments. The maximum shear stress of the bed surface is 0.752 Pa based on the ISWs equation (Table 3), larger than the threshold starting shear stress. In summary, the second equation is more consistent with the results of this experiment. So, in consideration of the influence of seepage, the second set of equation should be selected.

Furthermore, Spearman and Manning (2008) have demonstrated that the threshold shear stresses for both deposition and erosion can operate simultaneously. The settling velocity could also be an important parameter for the erosion and waves tends to mix sediment homogeneously over the water depth (Spearman and Manning, 2008). However, bed forms and deposition were not discussed in the experiments.

If the seepage force is not considered, the threshold starting shear stress is 1.341 Pa. The maximum shear stress of the bed surface based on traditional and ISWs equations is smaller than the threshold starting shear stress. Therefore, sediments not resuspend in the experiment. It is calculated that after increasing the seepage force F_S, the threshold starting shear stress is reduced by 54.6%. Only when the seepage force is considered, the maximum shear stress is larger than threshold starting shear stress. Therefore, seepage force is critical for parameterization.

4.4 Mechanism

At present, the research on the interaction between ISWs and seabed sediments, including the shoaling and breaking process, and wave-induced resuspension, has been significantly developed in in-situ observations, laboratory experiments, and numerical simulations. Field observations in the South China Sea confirmed that ISWs could cause huge changes in seabed pressure in a short time (Ma et al., 2016). The sediment incipient motion is important for sediment transport and scour. The flow of pore water leads to different movement speeds between the pore water and the soil skeleton, and the existing relative speeds cause seepage and provide migration conditions for the internal fine-grained substances (Zhai et al., 2021a, b). The seepage in a porous seabed is an important parameter of seabed sediments. The transient excess pore water pressure is an important part of the pore pressure response of wave-induced seabed, which can cause vertical seepage in the shallow seabed (Guo et al., 2019). This process has been paid attention to in many research fields because the discipline boundaries are often described in different technical terms: subtidal pumps (Riedl et al., 1972; Shum and Sundby, 1996), pore water exchange (Precht and Huettel, 2004), permeation (Willetts and Drossos, 1975; Nielsen et al., 2001; Hoque and Asano, 2007), sediment-water interface exchange process (Friedrichs et al., 2006), wave pump (Santos et al., 2012) or generally described as the "seepage effect" (Baldock and Holmes, 1999; Myrhaug et al., 2014). These processes are all related to the transient seepage of the shallow seabed. Regarding the influence of wave-induced transient pore pressure response on the stability of the seabed, it is generally believed that when the wave crest passes by, an over-pressure effect relative to the mean water level will be generated in sediments, causing a downward seepage force (Chen et al., 2019). Those processes are also useful for seabed affected by ISW. As a result, the stability of the seabed increases, and erosion is inhibited. When the wave trough passes, an under-pressure effect relative to the mean water level will be generated in sediments, causing an upward seepage force. Therefore, the seepage can promote the sediment incipient motion near wave troughs (Zhai et al., 2021a). The stability of the seabed is reduced, and erosion is promoted.

Essentially, the transient pore pressure response corresponds to the elastic deformation of the seabed soil (Wang et al., 2014b; Chen et al., 2019), and the residual pore pressure response corresponds to the plastic deformation of the seabed soil (Sekiguchi et al., 1995). Excess pore water pressure originates from the elastic and plastic deformation of the seabed under external loads. The physical mechanism of this process corresponds to the vertical reciprocating transient seepage that enters and exits the seabed interface caused by the wave-induced transient excess pore water pressure (Guo et al., 2019; Zhai et al., 2021b). Fine-grained sediments in the shallow seabed are "sucked" into the overlying water column and become resuspended substances. The transient liquefaction of the wave-induced seabed triggers fine-grained sediments to "pump" upwards into the overlying water column and resuspend. Viscous sediments are poorly permeable and are susceptible to the transient seepage of the wave-induced seabed. This result is also consistent with the experimental results of this study. This experiment shows that there is a large seepage on the fine sand seabed, which has a significant impact on resuspension.

5 CONCLUSION

In this paper, a flume experiment is designed to divide the seabed into two parts to control the dynamic response of the seabed and thus control the seepage conditions. By manufacturing ISWs of depression and changing the seabed sediments and the amplitude of ISWs, the effect of seepage on the sediment resuspension by shoaling ISWs is compared and analyzed. However, we do not take into account other parameters of sediment in the paper. Experimental results show that seepage has a great influence on fine sand and can significantly promote sediment resuspension, and seepage can increase the amount of suspension by two times on average. However, seepage has little effect on the suspension of clayey silt and sandy silt. The reason is that seepage has a great influence on coarse-grained sediments, and fine-grained sediments are not susceptible to seepage due to their low permeability. Moreover, a seepage force is added to the traditional gravity, drag force, and uplift force, the parameterization of threshold starting shear stress of coarse-grained sediments is developed. The results of parameterization are verified, and the seepage force is found to be critical for parameterization. The physical mechanism of the process corresponds to the vertical reciprocating transient seepage that enters and exits the seabed interface caused by the wave-induced transient excess pore water pressure. The seepage promotes the sediment incipient motion near wave troughs.

This is a quantitative study on seepage for shear stress of coarse-grained sediments induced by ISWs, which is critical to geohazard and submarine landslide assessment. This study focuses on the parameterization of the threshold starting shear stress of coarse-grained sediments induced by ISWs. Future work will be devoted to verifying the results of this parameterization in the field.

6 DATA AVAILABILITY STATEMENT

All the data is available from corresponding authors, please contact zhuangcaitian@163.com.

7 ACKNOWLEDGMENT

The authors thank Dr. Dongsheng JENG from Griffith University for experimental setup.